Stability analysis of digitally controlled LCL‐type grid‐connected inverter considering the delay effect

Abstract

Owing to LCL-filter resonance, a single loop may not be adequate to stabilise the digitally controlled LCL-type grid-connected inverter, thus the capacitor-current-feedback active damping is usually introduced. However, the computation and pulse-width modulation delays of the digitally controlled system significantly affect system stability and damping performance. Moreover, the delay varies when the duty-ratio update instant and sampling instant are changed. In this study, the Nyquist diagram is used to investigate the system stability taking into consideration the delay effect in the continuous domain. Then, the general conclusions and formulas can be drawn: if the LCL-filter resonance is above the critical frequency, the Nyquist diagram of single loop may not encircle the critical point, and therefore stabilise the system; and if it is below, a damping strategy is required. However, given the delay effect, the active damping loop may be unstable, and two unstable open-loop poles will be generated in the grid current loop under certain conditions. Then its Nyquist diagram should encircle the critical point to ensure the system is stable. Furthermore, the restriction of the cross-over frequency discussed. Experimental results based on a 5 kW prototype have been provided to verify the theoretical analysis.

Stability of LCL-filtered grid-connected inverters with capacitor current feedback active damping considering controller time delays

“…They also proposed a design method for a digital controller in the two stable regions. Similar conclusions were also drawn in [13,14]. However, these papers do not provide sufficient explanation of the inherent relationship between active damping and controller time delays.…”

“…Despite a vast amount of literature that has been published on the subject of LCL filter in grid-connected inverters, there is still no consensus on a stability evaluation method accounting for computation and pulse width modulation (PWM) delays [11][12][13][14][15][16][17]. Reference [11] presented pioneering research on active damping in discretetime domain taking time delays into account, and concluded that discrete-time active damping is not always stable, depending on the ratio of resonance frequency to sampling frequency.…”

LCL-resonance damping strategies for grid-connected inverters with LCL filters: a comprehensive review

“…For instance, with one-sample delay (i.e., T d = T s ), the resonance still exists if a is between 1/6 and 1/2, as also analyzed in [26][27][28][29][30][31][32]34]. If (10) is fulfilled, the feedback AD in Fig.…”

“…AD strategies based on feedback compensation are in essence the same while their differences mainly lie in the choice of states for feedback. Typical applications of proportional i C1 feedback can be found in [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. For 1 storder derivative feedback of u C1 , a high-pass filter (HPF) with a similar response is an alternative solution [35].…”

“…Filter-based AD improves stability by adding a digital filter next to the current controller [11][12][13][14][15][16]. For feedbackbased AD, the state used for feedback can be the capacitor current [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], the capacitor voltage [33][34][35][36], the inverterside current [37], the grid current [38][39][40][41] or a combination of multiple states [42][43][44][45][46][47][48][49][50]. Among the feedback-based AD methods, proportional feedback of capacitor current is widely studied during last decade due to its simple implementation.…”